Robuster Combiners for Oblivious Transfer

Danny Harnik, Joe Kilian, Moni Naor +2 more

Chin‐Chen Chang, Jung-San Lee

Ganugula Umadevi, Sarat C. Addepalli, Kannan Srinathan

A robust combiner for a cryptographic primitive gives a secure implementation of the primitive when at least some of the input candidates are secure. Such constructions provide robustness against insecure implementations and incorrect assumptions underlying the candidate schemes. Robust combiners are useful tools for ensuring better security in applied cryptography. Combiners from the perspective of threshold schemes have been previously studied. However, such threshold schemes typically fail to capture all possible scenarios. In this paper, we characterize the possibility of a transparent black-box combiner for oblivious transfer (OT), given an access structure over the candidate implementations. We also propose a circuit-based framework for the construction of such combiners, and hence reduce the problem of optimal OT combiners to circuit optimization.

Danny Harnik, Joe Kilian, Moni Naor +2 more

A (1,2)-robust combiner for a cryptographic primitive P is a construction that takes two candidate schemes for P and combines them into one scheme that securely implement P even if one of the candidates fails. Robust combiners are a useful tool for ensuring better security in applied cryptography, and also a handy tool for constructing cryptographic protocols. For example, we discuss using robust combiners for obtaining universal schemes for cryptographic primitives (a universal scheme is an explicit construction that implements P under the sole assumption that P exists). In this paper we study what primitives admit robust combiners. In addition to known and very simple combiners for one-way functions and equivalent primitives, we show robust combiners for protocols in the world of public key cryptography, namely for Key Agreement(KA). The main point we make is that things are not as nice for Oblivious Transfer (OT) and in general for secure computation. We prove that there are no “transparent black-box ” robust combiners for OT, giving an indication to the difficulty of finding combiners for OT. On the positive side we show a black box construction of a (2, 3)-robust combiner for OT, as well as a generic construction of (1, n)-robust OT-combiners from any (1, 2)-robust OT-combiner.

Enrique Larraia

Yohei Kawamoto, H. Yamamoto

Secret function sharing schemes (SFSS), .which are first studied in (l), are defined and analyzed information theoretically. They are also extended to ramp schemes in the same way as (2). Furthermore, it is shown that an unconditionally secure distributed oblivious transfer (OT) protocol is constructed by combining the SFSS with multi-groups secret sharing scheme (MG-SSS) (3) and the protocol is more robust against collusion attacks than that shown in (4).